The Vice Presidency, as was noted, is notorious for being weak.
Except for breaking ties in the Senate and serving as President during a crisis, he has no real power.
So, here's a proposal:
Make the Vice President the head of the State Department.
Everything that Colin Powell does, Dick Cheney could do. All the diplomatic missions, bureuacratic wrangling, etc. could easily be assigned to a VP.
If this was the case in the Clinton years, Gore could say, "I actually ran something."